Can you convict a man of murder when all you have is a confession?

There's nothing corroborating his statements. He just said he did it, 33 years ago, and he's a man with [perhaps?] mental illness. This is Pedro Hernandez, arrested in the Etan Patz case. People want to believe that at long last, we have the answer and a man to punish, but do we really know?

“You want to make sure he’s not a chronic confessor,” the [unnamed] detective said. Many books are about those who confessed to crimes they did not commit...

“You always go back for more detail, more detail, more detail,” [said  Vernon J. Geberth, a retired New York City police lieutenant commander in the Bronx]. “The confession is usually devoid of a lot of facts. They just want to get it out. Once it’s out, the barrier has been crossed.” The need to confess behind him, the suspect may relax. “Get him something to eat, something to drink. ‘By the way, did you speak to anybody? Did you go to work the next day, or take the day off?’ Important things.”...

The detective I spoke with said he would return to [the people who worked at the bodega in 1979] and find others. “What he said to them, when he said it, what details he gave. What was his demeanor? Has he ever admitted to doing anything else?... Corroboration is such a legal thing, it’s a thin requirement... The question is, do you get the jury to believe this is the real thing?”

The detective stresses getting a conviction, but we need to also worry about what is actually true.